If the random variable X is normally distributed with mean and standard deviation , then the random variable Z defined by is also normally distributed with mean 0 and standard deviation 1.

Question

If the random variable X is normally distributed with mean  and standard deviation  , then the random variable Z defined by  is also normally distributed with mean 0 and standard deviation 1.

Quizplus · Accepted Answer

Standardizing a normal distribution by subtracting the mean and dividing by the standard deviation results in a new normal distribution with mean 0 and standard deviation 1, regardless of the values of the original mean and standard deviation. Therefore, if X is normally distributed with mean μ and standard deviation σ, then Z = (X - μ) / σ is also normally distributed with mean 0 and standard deviation 1.

If the Random Variable X Is Normally Distributed with Mean